Differentiate trigonometric functions

Question

The question is to Differentiate the following with respect to x

\begin{align} Q1. \sin^3x \end{align}

The answer given is \begin{align} 3\sin^2x \cos x \end{align}

I am not sure how they got this answer so any help would be appreciated.

Answer 1

Use the Chain Rule, where the derivative of $f(g(x))=f'(g(x))g'(x)$.

Let $f(x)=x^3$ and $g(x)=\sin(x)$, so that $f(g(x))=(\sin(x))^3$.

Apply the chain rule to get $3\sin^2(x)\cos(x)$.

Answer 2

HINT: Rewrite $\sin^3x$ as $(\sin x)^3$ and apply the chain rule.